byeong-joo lee cmse.postech.ac.kr. byeong-joo lee cmse.postech.ac.kr scope fundamentals 1.free...

Byeong-Joo Lee cmse.postech.ac.kr


ScopeScope

Fundamentals

1. Free Surfaces vs. Grain Boundaries vs. Interphase Interfaces

2. Concept of Surface Energy/Surface Tension 3. Origin of Surface Energy and its Anisotropy4. Grain Boundary/Interfacial Energy

Interface Phenomena

1. Curvature Effect2. Multi-component system • Segregation3. General

• Grain Growth • Morphological Evolution

4. Interface Engineering


SurfacesSurfaces


Fdxdxl 2l

F

2

PTA

G

,

dAVdPSdTdG

Concept of Surface Energy and Surface Concept of Surface Energy and Surface TensionTension for liquid film

Generally,

AγGG 0 dAFAdγdAdG Tension Surface

dA

dAγF Tension Surface


A

s

N

Hw

42

3

As ZNH 5.0

15.13

2

)111(

)100(

For Cu: a = 3.615 Å △Hs =337.7J/mol γ(111) = 2460 erg/cm2 (1700 by expt.)

For fcc ※ Origin of Anisotropy

Pair approximation

Necessary Work for Creationof (111) surface in fcc (/atom)

For fcc (111): N/A = 4/(31/2a2) fcc (100): N/A = 2/a2

Estimation of Solid Surface Energy Estimation of Solid Surface Energy -- Origin of Surface Origin of Surface EnergyEnergy

A

N

N

H

A

s

4


Comparisons Comparisons

High Index Surface EnergyHigh Index Surface Energy

1. W.R. Tyson and W.A. Miller, Surf. Sci. 62, 267 (1977).2. L.Z. Mezey and J. Giber, Jpn. J. Appl. Phys., Part 1 21, 1569 (1982).

Estimation of Solid Surface Energy Estimation of Solid Surface Energy -- Orientation Orientation dependencedependence


Equilibrium shape of a Crystal Equilibrium shape of a Crystal -- WulffWulff constructionconstruction


Equilibrium shape of a Crystal Equilibrium shape of a Crystal - Numerical - Numerical ExampleExample

102

22 c

caES

2

122

a

c

.4

22 const

caA

cc

afor

2

2210


Note Note - Estimation of Surface Energy- Estimation of Surface Energy

J. Park, J. Lee, Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 135–141


Grain Boundary / Interface

Atomistic Computation of Surface EnergyAtomistic Computation of Surface Energy


Grain

Boundaries

Grain

Boundaries


Grain boundaries in Solids Grain boundaries in Solids - Misorientation- Misorientation

(RD) 1x

TD)(2x

ND)(3x

cx2

cx1

cx1

cx1

cx1

cx1

cx1

cx2cx2

cx2

cx2

cx2

cx3

cx3

cx3

cx3

cx3

cx3

MisorientationMisorientation

vs.vs.

InclinationInclination


Grain boundaries in Solids Grain boundaries in Solids - tilt vs. twist - tilt vs. twist boundariesboundaries

D

1γ


[100] Twist Boundary Structure in pure Cu[100] Twist Boundary Structure in pure Cu

33oo 4 4oo 7 7o o 10o

1515oo 20 20oo 30 30o o 45 45o


[100] Twist Grain Boundary Energy of [100] Twist Grain Boundary Energy of CopperCopper


Special High-Angle Grain BoundariesSpecial High-Angle Grain Boundaries


· Incoherent boundary energy is insensitive to orientation. ※ Special boundaries with low energy

[100] and [110] tilt Boundary energy of [100] and [110] tilt Boundary energy of Al Al

Special High-Angle Grain BoundariesSpecial High-Angle Grain Boundaries


2

31

3

12

1

23

sinsinsin

Equilibrium Microstructure Equilibrium Microstructure - balance of GB - balance of GB tensionstensions

θ

LV cosLVLSSV

LS SV


Normal Grain Growth Normal Grain Growth - the mechanism- the mechanism


Effect of particles on Grain Growth Effect of particles on Grain Growth - Zener - Zener pinning effectpinning effect

0max 45, rF sincosr2F

Consider the balance between the dragging force (per unit area)

and the pressure from the curvature effect

• dragging force due to one particle of size r

• number of ptl. per unit area of thickness 2r

⇒ drive it !

• total dragging force per unit area

2r2

3f

D

2γ

2r

3fγπrγ

2ππ

3fP

2

3f

4rDmax • Maximum grain size


Interphase

Interfaces

Interphase

Interfaces


Interfaces in Solids Interfaces in Solids – Coherent, Semi-Coherent & Incoherent – Coherent, Semi-Coherent & Incoherent InterfacesInterfaces

chγ

defchγ

δ

dD β

α

αβ

d

ddδ

δdef


from Y.S. from Y.S. YooYoo

KIMSKIMS

Interfaces in Solids Interfaces in Solids – Shape of Coherent Second-– Shape of Coherent Second-Phase Phase

min.γAΔG iistrain )(

※ Equilibrium Shape


γ’ precipitates of Ni-Al alloy system, D.Y. Yoon et al. Metals and Materials

Strain Energy vs. Interfacial Energy Strain Energy vs. Interfacial Energy - Mechanism of particle - Mechanism of particle splittingsplitting

Phase Field Method Simulation

by P.R. Cha, KMU


Morphological Evolution Morphological Evolution - from Y.S. Yoo, - from Y.S. Yoo,

KIMSKIMS


Interfaces

Phenomena

Interfaces

Phenomena


QuestionQuestion

Interfacial Phenomena(Interface or Surface Segregation)

Thermodynamics of Surface or Grain Boundary Segregation 1. M. Guttmann, Surf. Sci., 53 (1975) 213-227; Metall. Trans. A, 8A (1977) 1383-1401. 2. T. Tanaka and T. Iida, Steel Research, 65, 21-28 (1994).


Interfacial Phenomena Interfacial Phenomena – Segregation (Guttmann)– Segregation (Guttmann)

iiiiio XRTG ln

Assume a one atomic layer surface phase and consider equilibrium between bulk and surface

RTGBn

Bi

n

i seg

eX

X

X

X /

where ωi is the molar surface areaAssume ωi = ωj = … = ω

Bi

Bi

Bi

Bi

o XRTG ln

Biifrom

1

1

/

/

)1(1n

j

RTGBj

RTGBi

isegj

segi

eX

eXXnentsmulticompofor

Bi

iBi

iBi

oi

o

X

XRTRTGG

lnln][

Bin

BniB

no

noB

io

ioseg RTGGGGG

ln][][


Interfacial Phenomena Interfacial Phenomena – Segregation (Physical Meaning of Quantities)– Segregation (Physical Meaning of Quantities)

Biifrom

Bi

iBi

iBi

oi

oi X

XRTRTGG

lnln][

][][

ln][][

Bn

xsBi

xsn

xsi

xs

no

io

Bin

BniB

no

noB

io

ioseg

GGGG

RTGGGGG

Bi

i

i

Bi

xsi

xs

i

Bi

oi

o

i X

XRTGGGG

ln][

1][

1


Interfacial Phenomena Interfacial Phenomena – Segregation (Butler/Tanaka)– Segregation (Butler/Tanaka)

ji

RTGXXXX segi

Bnn

Bii ni ////ln '

11

)/ln(][1

][1

)/ln(][1

][1

Bnn

n

Bn

xsn

xs

n

Bn

on

o

n

Bii

i

Bi

xsi

xs

i

Bi

oi

o

i

XXRT

GGGG

XXRT

GGGG

)/ln()/ln(][1

][1

][1

][1 B

nnn

Bii

i

Bn

xsn

xs

n

Bi

xsi

xs

i

Bn

on

o

n

Bi

oi

o

i

XXRT

XXRT

GGGGGGGG

RTGBnn

Bii

segi

n

i

eXXXX ///

][][][][Bn

xsn

xs

n

iBi

xsi

xsBn

on

o

n

iBi

oi

osegi GGGGGGGGG


Thermodynamic Calculation of Surface Tension of Liquid AlloysThermodynamic Calculation of Surface Tension of Liquid Alloys

on the Web-board of this Lecture


Thermodynamic Calculation of Surface Segregation in Solid AlloysThermodynamic Calculation of Surface Segregation in Solid Alloys


Key PointKey Point

Surface/Interface Energy of Crystalline Solids

is Anisotropic


Pure W W + 0.4wt% Ni

Vaccum Annealing

An issue for thinking An issue for thinking - Surface Transition and Alloying - Surface Transition and Alloying EffectEffect


Abnormal Grain Growth Abnormal Grain Growth – – Mechanism ?Mechanism ?


Abnormal Grain Growth Abnormal Grain Growth – from N.M. Hwang – from N.M. Hwang


Wetting angle : 36o Wetting angle : 120o

Fe - 0.5% Mn – 0.1% C, dT/dt = 1 oC/s

from SG Kim, Kunsan University

Phase Field Simulation of Phase Field Simulation of γ→αγ→α transformation in transformation in steelssteels


Grain Boundary Identification SchemeGrain Boundary Identification Scheme

(RD) 1x

TD)(2x

ND)(3x

cx2

cx1

cx1

cx1

cx1

cx1

cx1

cx2cx2

cx2

cx2

cx2

cx3

cx3

cx3

cx3

cx3

cx3

How to uniquely define misorientation and inclination between two neighboring grains

H.-K. Kim et al., Scripta Mater.

(2011)


Sigma (Σ) Theta (θ) (hkl) plane Sigma (Σ) Theta (θ) (hkl) plane5 36.87 100 11 144.9 3103 70.53 110 5 180 310

11 50.48 110 7 115.38 3109 38.94 110 3 146.44 3113 60 111 9 67.11 3117 38.21 111 11 180 3113 131.81 210 5 95.74 3119 96.38 210 11 100.48 3207 73.4 210 7 149 3205 180 210 7 180 3213 180 211 9 123.75 3215 101.54 211 9 152.73 322

11 62.96 211 11 82.16 3317 135.58 211 7 110.92 3319 90 221 5 154.16 3315 143.13 221 11 180 332

Grain Boundary Energy of BCC FeGrain Boundary Energy of BCC FeH.-K. Kim et al., Scripta Mater.

(2011)


Phase field simulation of grain growthPhase field simulation of grain growth

- Isotropic GB mobility- Random crystallographic orientation vs. weakly-textured orientation (LAGB = 1.4 % vs. 4.9 %)

- Isotropic GBE - Anisotropic GBE (realistic GBE

DB)

H.-K. Kim et al.

(2013)


Effect of Anisotropic GBE and Precipitates on Effect of Anisotropic GBE and Precipitates on Abnormal GGAbnormal GG

C.-S. Park et al., Scripta Mater. (2012)


Interface Engineering

Case Study

Interface Engineering

Case Study


{100} textured steel sheets {100} textured steel sheets

Widely used electrical steel: {110}<001> Goss texture

•<001> is a “soft” magnetic direction ⇒ reduction of energy

loss

Why {100} textured steel sheets?

•Much improved magnetic properties (magnetic induction and core

loss) are expected in {100}<001> cube textured electrical steels

•Twenty-times high price compared to Goss texture


SurfaceBulk

ConcentrationAve. Concentrationwithin a unit cell distance from

surfaceSurface E, J/m2

(100) 0.01% 30% 0.80

(110) 0.01% 12% 1.61

(111) 0.01% 27% 1.43Esurf of pure Fe = 2.50, 2.35, 2.56 for (100), (110), (111)

(100) 0.1% 34% 0.65

(110) 0.1% 17% 1.34

(111) 0.1% 30% 1.00

Change of Surface Energy Anisotropy due to Surface Segregation

Atomistic Approach Atomistic Approach - surf segregation vs surf energy


Phase Field Simulation of Grain Growth Phase Field Simulation of Grain Growth – steel sheet


Construction of Surface Energy DatabaseConstruction of Surface Energy Database

SurfaceSurface concentration

of phosphorus (1100 K)

Surface energy of pure bcc Fe

(0 K)

Surface energy for bcc Fe-P

alloy(0 K)

1 (100) 0.336 2515 649

2 (016) 0.352 2535 545

3 (116) 0.388 2551 482

4 (012) 0.318 2506 1085

5 (136) 0.292 2519 1334

6 (112) 0.276 2459 1041

7 (034) 0.332 2444 1179

8 (134) 0.311 2470 1304

9 (234) 0.323 2553 915

10 (334) 0.369 2561 705

11 (110) 0.270 2355 1336

12 (166) 0.332 2443 1216

13 (122) 0.307 2541 899

14 (233) 0.293 2554 1076

15 (111) 0.301 2572 1002


Red

Yellow

8,000steps (0.75sec)

Initial sample

assuming that impurity atoms were segregated before the

grain growth

Phase Field Simulation of Grain Growth Phase Field Simulation of Grain Growth – modified

How to realize the simulation condition in experiments

at 1173 K


Experimental Verification Experimental Verification – {100} texture on Steel Sheet

Future work: Generation of {100}<001> cube texture


Hydrogen flux through a palladium-coated vanadium composite-metal membrane as a function of operating time.D. J. Edlund, J. McCarthy, J. Membrane Sci. 107, 147 (1995)

Degradation of permeability due to interdiffusionDegradation of permeability due to interdiffusion

Pinhole -> V layer exposed -> oxidationPinhole -> V layer exposed -> oxidation

S. I. Jeon, J. H. Park, E. Magnone, Y. T. Lee, E. Fleury, Current Applied Physics 12, 394 (2012)

V Catalytic coatinglayer of Pd (~150nm)

Design of Sustainable Hydrogen MembranesDesign of Sustainable Hydrogen Membranes

Experimental information on Y effect

Microstructure of V alloys after 10 hours of H permeation test at 400ºC

Eric Fleury (Center for High Temperature Energy Materials, KIST)


Element Site 1 Site 2 Site 3

Pd 0.0713 -0.29912 -0.29091

Al 0.3678 0.1201 -0.1370

Cr -0.2839 0.1188 -0.0258

Y 0.59198 -0.2041 1.01056

- Interatomic potential : 2NN MEAM (ternary V-Pd-Y) W.-S Ko and B.-J. Lee, MSMSE (2013)

- Temperature : 1100K - Bulk concentration of Y : 0.07at% - Number of MCS : 20,000 steps

V

Y

Segregation Tendency of Y on GBs of bcc V Segregation Tendency of Y on GBs of bcc V

Atomistic GCMC simulation of Y segregation on GB of vanadium

{110} tilt 71°(Σ3)

unit : eV

First-Principles Calculationof GB binding energy

- Code : VASP- Pseudo potential : PAW method, GGA- Number of atoms in a cell : 116- K-point : 4×1×3- Cutoff energy for P-W basis : 300 eV- Vacuum region : 11Å for-y direction- Cell dimension : Fixed- Atomic relaxation : Allowed- Convergence criteria for energy and force : 0.001 meV and 10 meV/Å, respectively


V84.8Ni15Y0.2 : pre-annealing(X) V84.8Ni15Y0.2 : pre-annealing(O) V84.8Ni15 : pre-annealing (O)

Pre-annealing vs. Grain Growth ?

Pre-annealing > Reduction of GB

- Gas : H2

- Temperature : 753 K - Time : 12 days - Annealing Temp: 1473 K - Annealing Time : 1 day

Experimental VerificationExperimental Verification – Effect of GB segregated – Effect of GB segregated YY

J.-H. Shim et al., KIST

Perform a pre-annealing before Pd coating Perform a pre-annealing before Pd coating to maximize GB segregation of Yto maximize GB segregation of Y

byeong-joo lee cmse.postech.ac.kr. byeong-joo lee cmse.postech.ac.kr scope fundamentals 1.free...

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